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The reaction given is:

\[
\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)
\]

We need to calculate the equilibrium constant, \( K_p \), using the partial pressures at equilibrium.

The expression for \( K_p \) for this reaction is:

\[
K_p = \frac{P_{\text{HCl}}^2}{P_{\text{H}_2} \times P_{\text{Cl}_2}}
\]

Where:
- \( P_{\text{H}_2} = 68.3 \, \text{atm} \)
- \( P_{\text{Cl}_2} = 52.4 \, \text{atm} \)
- \( P_{\text{HCl}} = 40.3 \, \text{atm} \)

Plugging these values into the equation:

\[
K_p = \frac{(40.3)^2}{68.3 \times 52.4}
\]

Let's calculate it step by step:

1. Calculate \( (40.3)^2 \):

\[
(40.3)^2 = 1624.09
\]

2. Calculate the denominator \( 68.3 \times 52.4 \):

\[
68.3 \times 52.4 = 3577.72
\]

3. Now calculate \( K_p \):

\[
K_p = \frac{1624.09}{3577.72} \approx 0.454
\]

Rounding to two significant digits:

\[
K_p \approx 0.45
\]

So the value of the equilibrium constant \( K_p \) is **0.45**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to expand your understanding:

1. How does changing the temperature affect the value of \( K_p \)?
2. What would happen to the equilibrium if additional hydrogen gas (\(\text{H}_2\)) was added to the system?
3. How does \( K_p \) differ from \( K_c \), and how can you convert between them?
4. If the pressures of the gases were in different units, how would you standardize them for the calculation?
5. How would a catalyst affect the equilibrium concentrations of the reactants and products?

**Tip**: Remember that \( K_p \) is dependent on temperature, so any changes in temperature can either increase or decrease its value depending on whether the reaction is exothermic or endothermic.

Hydrogen and chlorine react to form hydrogen chloride, like this: H2(g) + Cl2(g) → 2HCl(g). Also, a chemist finds that at a certain temperature, the equilibrium mixture of hydrogen, chlorine, and hydrogen chloride has the following composition: H2 = 68.3 atm, Cl2 = 52.4 atm, HCl = 40.3 atm. Calculate the value of the equilibrium constant Kp for this reaction. Round your answer to 2 significant digits.

Learn how to calculate the equilibrium constant Kp for the reaction between hydrogen and chlorine forming hydrogen chloride. Using the partial pressures of H2, Cl2, and HCl (68.3 atm, 52.4 atm, and 40.3 atm, respectively), this example walks through the steps to calculate Kp with a detailed explanation.

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